The function in the graph is a parabola that opens upward. To determine its range, we need to find the lowest value the function reaches (the minimum) and note that the function increases without bound from that point.

1. Vertex (Minimum Point):
   The lowest point on this parabola is at $y = -4$, which occurs around $x = 3$. This is the vertex of the parabola.

2. Range of the Function:
   Since the parabola opens upwards, the function can take any value from $-4$ upwards, meaning the range of the function is: $\boxed{[-4, \infty)}$

Would you like more details about parabolas, or do you have any other questions?

Related Questions:

1. What is the domain of this function?
2. How do you determine the vertex of a parabola from its equation?
3. What does the axis of symmetry represent in a parabola?
4. Can the range of a quadratic function ever be unbounded below?
5. How do we determine if a parabola opens upward or downward?

Tip:

For any quadratic function of the form $y = ax^2 + bx + c$, if $a > 0$, the parabola opens upwards, and if $a < 0$, it opens downwards.